It is completely up to you, but I think that inapplicable plausibilities should be a plausibility; It is just that, in order to avoid contradictions, "plausibility" shouldn't be defined as what can be applicably known, just what one believes is "true" — Bob Ross
I agree with this! I got caught up in my own verbiage, and need to separate the inductions by the ability to apply applicable knowledge, that I forgot one does not believe one can applicably know something to believe it is real.
On a separate note, the potentiality of a belief would be differentiated between irrational inductions and all other forms (as in it is irrational if it has no potential). — Bob Ross
Here, I am very careful to not use the word potentiality, because I think it loses meaning as an evaluative tool in the inductive hierarchy. Colloquially, I think its fine. I understand what you mean. But the reason why I don't think it works in the hierarchy is because the inductive hierarchy is not trying to assert what has more potential of being true, only which induction is more rational.
I believe this is a very important distinction. Recall that what is applicably known is based upon our context as well. A very narrow context might lead us to some strange probabilities and possibilities. It doesn't mean they are potential, as reality may very well defy them. They are simply rational inductions based on the applicable knowledge we have at the time.
Further, potentiality is not something the hierarchy can objectively measure. Let say that in a deck of 52 cards, you can choose either a face card, or a number card will be drawn next. You have three guesses. Saying number cards is more rational going by the odds. But the next three cards drawn are face cards. The deck was already shuffled prior to your guess. The reality was the face cards were always going to be drawn next, there was actually zero potential that any number cards were going to be pulled in the next three draws. What you made was the most rational decision even though it had zero potential of actually happening.
Lets go one more step. Same scenario. Only this time, I didn't put any number cards in the deck, and didn't tell you. You believe I made an honest deck of cards, when I did not. You had no reason to believe I would be dishonest in this instance, and decided to be efficient, and assume the possibility I was honest. With this induction, I rationally again choose number cards. Again however, the potential for number cards to be drawn was zero.
An induction cannot predict potentiality, because an induction is a guess about reality. The conclusion is not necessarily drawn from the premises. Some guesses can be more rational than another, but what is rational within our context, may have zero potential of actually being. That being said, generally acting rationally is a good idea, because it is based on what we do applicably know about the world, versus what we do not. It is less uncertainty, but has no guarantee.
So, I do understand your intention behind using potentiality, and in the end, it might boil down to semantics and context. For the purposes of trying to provide a clear and rational hierarchy, I'm just not sure whether potentiality is something that would assist, or cloud the intention and use of the tool.
Whereas, on the contrary, electrons can have two spin states: up or down. However, unlike the previous 6-sided die example, the subject, if they are quantum inclined (:, will assume the electron is equally likely in both positions (thus, not assuming the law of noncontradiction in the same sense as before). — Bob Ross
Not to get too off on a tangent here, but I believe the only reason we calculate it as having both, is because it is equally likely they could be either prior to measurement. It is like calculating what would happen for each side of a six sided die prior to rolling the die. But perhaps we shouldn't wade into quantum physics for examples, as I believe it mostly to be a field of conceptual land mines in any conversation, much less while addressing a new theory of knowledge!
To say that the probability of 1/52 is more cogent than a possibility seems wrong to me, as I am extrapolating that from the possibility of there being 52 cards. — Bob Ross
Probability does not assert there are possibly 52 cards, it asserts that there are 52 cards, whether this be based on applicable knowledge or belief. Of course, what if I'm having a thought experiment? This is a great time to get into math.
Math is the language of discrete experience, and distinctive knowledge. 1, is "a discrete experience" One blade of grass. A field of grass. One piece of grass. It is the abstraction of our ability to discretely experience "a" thing. "Two" is the idea that we can create 1 discrete experience, and another discrete experience. The discrete experience of both together as one identity, is two.
Math is the logic of discrete experience. It is why it fits so well into our world view, because it is an abstraction of how we view the world. When I say, "two blades of grass," this relies on a context of two identities that are similar enough to be labeled "blades of grass". It does not assert their equality on a mass or atomic level. This is because it is an abstraction of our ability to contextualize identities down to their essential properties for the purposes of addition and subtraction, while throwing out all non-essential properties.
The proofs of math work, because they can be confirmed by our discrete experience being actively applied. Therefore I can abstract that if I have 20 bushels of hay, and take away 2 bushels of hay, I have 18 bushels of hay. I can discretely experience that in my head right now. I'm not claiming what constitutes a bushel. I have no need for the weight of each bushel down to the ounce, its color, smell, etc. I just need a discrete experience of a bushel, and this is enough to abstract something useful for reality.
Even so, just like language, math must be applied to reality without contradiction to be applicably known. I can predict that a feather will fall at 9.8 meters a second, but may find in my measurements it does not . I might state that my 5 bushels of hay at 20 pounds each will result in 100 pounds of hay, but upon actual measurement, I find they only weigh 98 pounds.
For example, if I have a function F(N) = N + 1, this is a mathematical induction but not a probability. So, is it a plausibility? Is it a possibility? — Bob Ross
This is a known function. This is an observation of our own discrete experience. If I take N identities, and add one more, then this will equal the identities added together. So, 2+1 are the same as the identity of 3. This applies to the abstract of discrete experience, which when applied to reality could specifically be bushels of hay, sheep, etc. As it is in its functional form, it is only a descriptive logic of discrete experiencing.
This leads to,
Thirdly, it also depends on how you define "apply to reality" whether that holds true. Consider the belief that you have thoughts: is your confirmation of that ever applied to "reality"? — Bob Ross
This goes back to the beginning of the essay. Recall that what we discretely experience, we know. That is because it is impossible to deny that we discretely experience. When I discretely experience something that I label as "thoughts" in my head, I distinctively know I have them. Applicable knowledge is when we apply our distinctive knowledge outside of our own ability to create identity as we wish. I might believe that the apple in front of me is healthy for me, but when I bite into it, I find it rotten. The apple is something apart from my own identifiable control in this way. Your thoughts are also reality.
Distinctive knowledge occurs, because the existence of having thoughts is not contradicted. The existence of discretely experiencing cannot be contradicted. Therefore it is knowledge. I label this special type of knowledge distinctive, because it is something within our control. I can create a world of magic and unicorns distinctively, but there is a limit when applied to that which I do not have control over, reality.
So, going back again to abstracting the idea of 1/52 playing cards, I can distinctively create the limitation in my head that there are 52 playing cards, that they are randomly shuffled, and 1 is pulled without applicably knowing which card it is. I can then establish the limitations of what the necessary possibilities are knowing what each card is within the deck. But, if I applicably apply this probability to any one particular deck in reality, what actually happens is what actually happens.
Perhaps some of the cards were not all the same weight or smoothness, and it causes some of them to stick in the shuffle. Perhaps there is some strange law of physics we didn't know about in reality that causes the Ace of spades to come up more frequently. Math is the ideal of distinctive knowledge, but it must still be applied to reality when it makes a prediction about a particular reality to see if it is applicably known.
Secondly, it seems a bit wrong to me to grant probabilities their own category when there can be plausible probability claims and possible probability claims. — Bob Ross
We cannot meaningfully understand what plausible probability is, without first distinctively and applicably knowing what plausibility, and probability are first. Recall then, that a plausible probability is a chain of reasoning. I have a plausibility, and from that plausibility, I assert a probability. I have a possibility, and from that I assert a probability. I have applicable knowledge, and from that applicable knowledge, I assert a probability.
If I could compare all three inductions, it would be most rational to use the one that has applicable knowledge as its base.
1. Its plausible the dark side of the moon is on average hotter than the light side of the moon, therefore it is probable any point on the dark side of the moon will be hotter than any point on the light side of the moon.
2. Its possible the side of the moon facing away from Earth is on average colder than the light side of the moon, therefore it is probable any point on the dark side of the moon will be colder than any point on the light side of the moon.
3. The dark side of the moon has been measured on average to be cooler than the light side of the moon at this moment, therefore it is probable any point on the dark side of the moon will be colder than any point on the light side of the moon.
As you can see, intuitively, and rationally, it would seem the close the base of the chain is to applicable knowledge, the more cogent the induction.
I think that it is an absolutely brilliant assessment! Well done! However, I think, although we have similar views, that there's still a bit to hash out. — Bob Ross
Thank you! Yes, please continue to drill into the theory as much as you can. Its usefulness is only as good as its ability to withstand critiques. Again, greatly enjoying the conversation, and my thanks for your pointed assessment and crticism!